Question

If 123 is subtracted from the square of a number, the answer so obtained is 976. What is the number? Short cut method

Answer 1

Hi there!
Here's the answer:

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Let the No. be x

x² - 123 = 976
=> x² = 123 + 976
=> x² = 1099
=> x = √1099

1089 < 1099 < 1156
33² < 1099 < 1156
33< √1099 < 34


No. of Non perfect Squares b/w 33² & 34² = 2a = 2×33 = 66

1099 - 1089 = 10
1156 - 1099 = 57

10 < 57

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√1099 = 34 + [(10/66)] =


=> √1099 =~ 34.15151515


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¶¶¶¶¶¶ Check this ¶¶¶¶¶¶¶


To find Square root of Non perfect square x

• Estimate it between known lower and upper consecutive squares

a² < x < b²
a < √x < b

• No. of Non perfect squares b/w a² & b²
= 2 × a

• Check whether No. is nearest to lower known square or Higher known Square
=> Find x-a & b-x

• Case-1 : If x-a is less
√ x = a + [(x-a)/2a]

• Case-2 : If b-x is less
√x = b - [(b-x)/2a]



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:)


Hope it helps